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Q.Briefly describe Error analysis in Runge kutta Fehlberg method.

Q.Briefly describe Error analysis in Euler method and Taylor series method.

Q.Briefly describe Euler method and Taylor series method.

Q. Prove Taylor series method.

Q. Prove Euler Method from taylor series method.

Q. Use Runge Kutta Fehlberg method with tolerance TOL=〖10〗^(-6), hmax=0.5, and hmin=0.05 to approximate the solutions to the following initial value problem. Compare the result to the actual value.

y^'=(t+〖2t〗^3)y^3-ty, 0≤t≤2,y(2)=1, y(0)=1/3 , actual solution y(t)=〖(3+2t^2+6e^(t^2 ))〗^(-1⁄2)

y^'=(t+〖2t〗^3)y^3-ty, 0≤t≤2,y(2)=1, y(0)=1/3 , actual solution y(t)=〖(3+2t^2+6e^(t^2 ))〗^(-1⁄2)

Q. Use Runge Kutta Fehlberg Algorithm with tolerance TOL=〖10〗^(-4) to approximate the solution to the following initial value problem.

y^'=sint+e^(-t), 0≤t≤1,y(0)=0,with hmax=0.25,and hmin 0.02

y^'=sint+e^(-t), 0≤t≤1,y(0)=0,with hmax=0.25,and hmin 0.02

Q. Use Runge Kutta Fehlberg method with tolerance TOL=〖10〗^(-4), hmax=0.25, and hmin=0.05 to approximate the solution to the following initial value problem. Compare the result to the actual value.

y^'=1+〖(t-y)〗^2, 2≤t≤3,y(2)=1, actual solution y(t)=t+1⁄((1-t)).

y^'=1+〖(t-y)〗^2, 2≤t≤3,y(2)=1, actual solution y(t)=t+1⁄((1-t)).

Write down the importnt Viva Questions and answers in Runge kutta method and R.K.F method

Q. List important viva short questions of RK merhod and RKF method.